Mechanical design of an upper limb robotic rehabilitation system

Abstract

Physical diseases have become an alarming social problem worldwide. Several conditions related to limb mobility are more frequent due to a high level of demand in the repetitive execution of activities. Assistive technologies have been proposed to improve the experience of physical rehabilitation. This paper presents a framework with the mechanical design criteria for an upper limb assistive robotic system. We define the design specifications and construction characteristics of an assistive system. As a result, a 7-degree-of-freedom system for upper limb physical rehabilitation is designed with a novel characteristic of arm-switching configuration for the treatment of both arms.

Keywords:

• Assistive robotics
• upper limb
• mechanical design
• FEA

1. Introduction

Physical impairments have become a social problem, that affect the performance of daily activities in people that suffer from these diseases, affecting their quality of life [1],[2]. Physical disabilities are caused by several factors such as aging, chronic diseases, and musculoskeletal disorders [1]. A high level of demand in the execution of repetitive or high-impact activities, or an accident at work, home, or traffic can also cause motor impairments such as tendinopathies, especially in upper limbs [2]–[4].

A physical rehabilitation process is required to restore a person socially, physically, and occupationally after suffering from any musculoskeletal disorder. To regain limb functionality, patients undergo treatments that increase the range of mobility, muscle strength, and chronic pain prevention [5]–[14].

As part of the rehabilitation process, assistive robotics has been developed to support physiotherapy treatments to provide an adequate and controlled intervention [15],[16]. The use of these technologies has increased due to the use of instrumentation to quantify variables such as range of movement, velocities, muscle activity, and force [17]–[19]. However, the development of robotic devices involves mechanical design to a large extent and depends on the patient’s prognosis, dimensions, and functionalities. Assistive systems are designed according to the biomechanical characteristics of the required joint and the limb. From the anatomical viewpoint, it is complex to design an exoskeleton that shares perfect coupling with the joint, preserving the range of motion. Limitations can appear and remain in loss of mobility ranges, usually to avoid the collision of the robotic system with the patient.

In the literature, we find exoskeletons or end-effector-based, the first ones are better adapted to the human anatomy, and the latter allows a bilateral configuration without the need for a complex design and without having to duplicate the system for the opposite limb. Now, the question is which of the two configurations allows a better adaptation to the physical rehabilitation processes, and how can we join the advantages of each one. The mechanical design must respond to the minimum specifications of movement of the joints included in the different diagnostic and rehabilitation protocols, which leads to the selection of joints, ranges of mobility, and degrees of freedom in the design of the robotic system. In this paper, we propose a mechanical design of an assistive robotic system of 7 degrees of freedom to support the therapy of elbow tendinopathies. Medical criteria have been considered as part of the formulation and development of the mechanical design. We present a novel design of anthropometric adjustment and arm-changing configuration, avoiding the need to duplicate the robotic arm.

Relevant works of mechanical design for physical rehabilitation purposes have been presented. For example, in [20], an exoskeleton (ANYexo) has been developed in which the range of motion (ROM) is optimized to mimic the interaction of therapists. Or in [21], tensegrity is proposed to approximate real movements accurately. Similarly, in [22], mechanical postural synergies are developed to reduce the complexity of transmission mechanisms. Another example is the TTI-Exo [23], which has adjustable link lengths to partially align the human and exoskeletal joints to avoid uncontrolled forces caused by hyperstaticity. In this case, the limitation remains in the loss of mobility ranges, usually to avoid the collision of the robotic system with the patient [20],[24].

Furthermore, material selection plays an important role in the design of lighter and more compact systems as the one proposed here. It implies considering features like lightness, robustness, hardness, and durability. Moreover, the material selection is based on the biomechanical characteristics of the joint to be treated. Mechanical rehabilitation systems used to be manufactured in materials such as stainless steel, titanium or aluminum, ceramics, polymers, composites, or biomaterials according to the standards in the selection of materials for manufacturing medical devices and equipment such as ISO 10993-1, and safety and performance as IEC 60601-1 [25]–[28]. However, plastics and composites have become interesting options for part manufacturing because they can be molded into useful configurations that would be difficult or impossible to duplicate in metals and can be fabricated using technologies such as 3D printing. Some works reported interesting variations, such as the design of lightweight devices built in 3d [29] and lightweight exoskeletons as proposed by [30]. Other examples, such as the CRUX system (Compliant Robotic Upper-extremity eXosuit) [21] and Co-Exos [31] are highlighted. Carbon-based polymer composites are increasingly being used to design rehabilitation robotic systems because of their ease of fabrication compared to metals. For example, the CLEVERarm [32],[33] has links made of 3D printed carbon fiber reinforced plastic for a lightweight and compact design. The use of carbon fiber-reinforced links for upper limb exoskeletons has already been explored. For example, the carbon fiber reinforced links of the LEXOS exoskeleton [34] were manufactured using the vacuum bag technique.

On the other hand, assistive systems have been designed bilaterally or with an option to switch arms. For end-effector-based systems, bilateral design and implementation are much simpler because the anchor point between the system and the upper limb is usually through the hand grip. Works such as [35]–[40] have implemented bilateral training in end-effector-based systems. For the case of exoskeletons, the design is complex, and some authors opt to duplicate the robotic system by adapting it for the opposing limb as [23],[41]. Alternatively, the same system for one limb can be adapted for the opposite limb using an arm-switching configuration. In this way, it reduces costs and adds attributes in terms of adaptability, especially if used in physical rehabilitation applications. The best-known system with this configuration is the Armeo Power system by Hocoma [42],[43]. Nevertheless, to the best of our knowledge, there are no similar configurations besides the Armeo Power.

This article proposes a robotic assistive system that uses multiple limb joints through the conceptual and engineering design of a 7-degree-of-freedom assistive system to support the diagnosis and rehabilitation processes of elbow tendinopathies. Within the requirements, mechanical rehabilitation designs should have adjustable joint spacing systems. Medical criteria have been considered for the formulation and development of the mechanical design, as suggested by [44]. We present a novel design of anthropometric adjustment and arms change configuration, avoiding the need to duplicate the arm. We analyze the physiology, biomechanics, and pathology of the upper limb. Thus, qualitative and quantitative design criteria are defined, determining the degrees of freedom and torques required according to specifications obtained from these criteria. Subsequently, we perform motion studies and material selection, and develop the mechanical design, showing the part-to-part description and the preliminary version together with the arm-switching configuration; finally, we present some conclusions of this work.

2. Physiology, biomechanics and tendinous pathologies of the upper limb

In this section, we present the fundamental concepts related to anatomy, physiology, tendinous pathologies, and physiotherapy exercises for the upper limb, to determine the system functionality and mechanical design criteria.

2.1. Anatomy, physiology, and biomechanics

The anatomy of the upper limb is reviewed, since this is the basis for the design of the assistive robot. The arm is a biomechanical system, which is fixed to the trunk by means of the shoulder girdle [45] and is composed of three parts: the arm, the forearm, and the hand [46].

The joint complex where the ends of the humerus, scapula, and clavicle bones meet is called the shoulder [47]. This is the most mobile joint in the entire human body as it allows the orientation of the upper limb in the three anatomical planes (sagittal, frontal, and transverse), which allows flexion-extension, adduction-abduction, internal-external rotation, and horizontal flexion-extension movements through the joints that make up the shoulder joint complex: subdeltoid, acromioclavicular, scapulothoracic, sternocostoclavicular and scapulohumeral [46],[48]. The latter also allows complementary protraction-retraction movements of the shoulder. The upper arm corresponds to the upper part of the limb. It is composed of the humerus, on which different triceps and biceps muscles are inserted in order to perform the movements produced from the shoulder. The arm is joined to the forearm through the elbow joint, where the humerus articulates with the ulna and radius [46],[49]. The elbow is the intermediate joint of the upper extremity. It is composed of three joints [45], which allow flexion and extension movements (humerus-ulna), distribute the load-bearing forces (humerus-radius), and transmit pronation and supination movements (ulna-radius) to the wrist [47]. In Figure 1, the main movements of the upper limb considered for mechanical design are presented.

Figure 1. Main movements of the upper limb considered for mechanical design.

The forearm is composed of two bones: the ulna and the radius, which in its proximal portion are joined to the humerus through the elbow, and in its distal portion to the carpals through the wrist. Due to the structure of the ulna, it does not perform rotational movements, however, unlike the ulna, the radius can rotate around a longitudinal axis, transmitting the rotational movement to the hand, which is known as pronation and supination movements [47].

Finally, the hand corresponds to the lower part of the limb, located at the end of the forearm, and goes from the wrist to the fingertips. It allows the tactile perception of objects, as well as their manipulation. The structure of the hand is formed by four parts, the carpus, the metacarpus, the palm of the hand, and the phalanges [46],[47]. It is important to note that the elbow joint complex within the therapy exercises, in addition to allowing its movement, also involves mobility in the other joints such as the hand and the shoulder [48]–[50]. Table 1 shows the evaluation of normal joint ranges and movements considered for each joint. Where two measurement methods are taken from AAOS (American Academy of Orthopedic Surgeons) in the United States and AO (Association for the Study of Osteosynthesis) in Europe. These articular ranges will allow defining the working space of the upper limb which will be the starting point in the design specifications of the robotic assistance system.

Table 1. Joints and ranges of mobility.

		Angles
Joint	Movement	AO	AAOS
Shoulder girdle	Protraction & Retraction		$0°-25°/30°$ & $0°-25°/30°$
Shoulder (glenohumeral)	Abduction & Adduction	$0°-160°/180°$ & $0°-30°$	$0°-180°$ & $0°$
	Flexion & Extension	$0°-150°/170°$ & $0°-40°$	$0°-180°$ & $0°-60°$
	Internal & External rotation	$0°-70°$ & $0°-70°$	$0°-70°$ & $0°-90°$
	Horizontal Flexion & Extension		$0°-135°$ & $0°-40°/50°$
Elbow	Flexion & Extension	$0°-150°$ & $0°-10°$	$0°-150°$ & $0°$
Wrist	Pronation - Supination	$0°-90°$ & $0°-90°$	$0°-80°$ & $0°-80°$
	Flexion & Extension	$0°-50°/60°$ & $0°-35°/60°$	$0°-80°$ & $0°-70°$

AAOS: American academy of orthopaedic surgeons and AO: Arbeitsgemeinschaft für osteosynthesefragen.

2.2. Tendinitis and physical therapy

The elbow joint is commonly exposed to repetitive movements that become pathologies [51], where the most common are elbow tendinopathies. These pathologies can occur at the level of the epicondyle (epicondylitis) or epitrochlea (epitrochleitis). This condition occurs frequently in people who practice sports such as tennis or golf, or for home or work activities that require constant and repetitive use [52].

Elbow tendinopathies are related to inflammation of the tendon structures that attach the muscles to the bony structures. Epicondylitis (tennis elbow), caused by repetitive motions that produce pain on the lateral aspect of the elbow near the external epicondyle at the origin of the wrist extensor muscles [53], and epitrocleitis (golfer’s elbow), inner side of the elbow, and is caused by an overload of the flexor and pronator muscles affecting the tendon insertion in the epitrochlea of the elbow due to hyperflexion movements [54],[55].

In all cases, a physical rehabilitation process is required to restore the person socially, physically, and occupationally after suffering any musculoskeletal disorder [5]–[8]. The main objective of physical rehabilitation is the prevention of rigidity and chronic pain, followed by the integration of the limb into their common motor patterns [51]. Once mobility, stability, and pain are controlled, the speed and strength are increased [56].

Within physical therapy, the specialist uses some tests to validate the diagnosis of tendinopathy and then uses other exercises for rehabilitation [6],[8],[57]. Exercise schemes used in the diagnosis and rehabilitation of tendinopathies require the elbow joint motion, as well as the other upper limb joint motion [58]. On the other hand, in common rehabilitation, stretching exercises are initially performed to recover flexibility, then mobility recovery exercises are performed, and finally, strength recovery exercises are performed [8]. In some recovery schemes, the movement of more than one joint is considered [6]. Tables 2 and 3 show the exercise schemes used for the diagnosis and rehabilitation of medial and lateral epicondylitis, where the joints involved, the movements, and the ranges of mobility are identified. Under that premise, the mechanical design must respond to the minimum specifications of joint motion included in the different diagnostic and rehabilitation protocols. This entails the selection of joints, mobility ranges, and degrees of freedom in the design of the robotic assistive system.

Table 2. Diagnosis test for lateral and medial Epicondylitis.

Diagnosis Lateral Epicondylitis	Joint Involved	Movement
Maudsley test	Wrist and elbow	Extension of the middle finger, opposite force applied and elbow in extension
Mills test	Wrist and elbow	Wrist flexion with ulnar deviation, progressive elbow extension
Chair test	Shoulder	Chair lift with the arm in extension and the forearm in pronation
Bowden test	Wrist	Arm in full extension and a slight extension of the wrist
Thompson test	Wrist	Closed hand extension, opposite force applied
Cozen test	Wrist	Closed hand extension, elbow fixed at approx. $90°,$ opposite force applied
Diagnosis medial Epicondylitis	Joint Involved	Movement
Test 1	Wrist	Wrist Flexion of the hand with fixed elbow, opposite force applied
Test 2	Wrist	Passive dorsal flexion
Inverted Cozen test	Wrist	Wrist Flexion of wrist extended in supination, opposite force applied
Golfer’s elbow sign	Elbow and wrist	Extension of the arm with palmar flexion of the wrist, opposite force applied
Extension test on the forearm	Elbow	Extension of the arm keeping the forearm in supination, opposite force is applied

Table 3. Rehabilitation exercises for lateral and medial Epicondylitis.

Rehabilitation lateral epicondylitis	Involved joint	Movement
Phase 1: Increased range of motion	Elbow and wrist	Stretching wrist extensors and flexors, pronation-supination of forearm, flexion-extension of wrist
Phase 2: Increased range of motion	Shoulder, elbow and wrist	Wrist extensor and flexor stretches, forearm pronation-supination, wrist flexion-extension, wrist grip
Phase 3: Increased strength	Shoulder, elbow and wrist	extensor and flexor stretching of the wrist, pronation-supination of the forearm, flexion-extension of the wrist, grip, isometric exercises
Rehabilitation medial epicondylitis	joint involved	movement
Stretching and flexibility for the musculotendinous unit	Shoulder and wrist	Stretching wrist extensors and flexors, pronation-supination of the forearm, flexion-extension of the wrist

3. Conceptual design and specifications

Based on the anatomy, physiology, and biomechanics of the upper limb, and on the diagnostic and rehabilitation exercises for elbow tendinopathies, the anatomical-mechanical model and the design specifications of the assistance system are determined.

3.1. Anatomical-mechanical analogy

To determine the anatomical-mechanical analogy between the upper limb and the robotic system, we start from the previously analyzed anatomical and functional parameters of the upper limb, where we then make a first approach to the design of the device in order to anthropomorphize the system based on the biological structure of the upper limb. In Figure 2 the diagram of the mechanical model approximation is presented.

Figure 2. Anatomical-mechanical analogy.

Anatomically, it is complex to design a system that shares the same alignment of the joint movement axes while conserving the maximum working space. In the literature there are some works that seek to improve the coupling conditions such as [21] where tensegrity to approximate real movements with greater precision is proposed, or as in [22] where postural mechanical synergies are developed to reduce the complexity of the transmission mechanisms, or in [20] where an exoskeleton (ANYexo) has been developed, in which the range of motion (ROM) is optimized to mimic therapist interaction. Another example is the TTI-Exo [23] which has adjustable link lengths to partially align human and exoskeletal joints in order to avoid uncontrolled forces caused by hyperstaticity, but the limitation remains in the loss of mobility ranges commonly to avoid collision of parts with the patient [20]. Ideally, the design of the system must ensure a perfect coupling between the robotic system and the human limbs in order to avoid discomfort or collisions [20],[24], but preserving to a greater extent the mobility ranges.

3.2. Qualitative and quantitative criteria

In addition to the analysis of biomechanics and mobility ranges, some qualitative and quantitative criteria are defined. Table 4 shows the criteria considered in the design of the robotic assistance system. These criteria allow the design specifications of the robotic assistance system to be established. The selection criteria are based on an exhaustive review of the existing literature on upper limb assistive systems, systems as [20]–[22],[29],[31],[35],[38],[41],[43],[59]–[81] are highlighted, where from the bibliographical analysis, the type of device, the type of chain and the type of transmission are highlighted and considered, and under this premise, advantages and disadvantages are defined. The other criteria considered are dimensional and functional specifications delimited according to the anthropometric and joint torque force parameterization consultation, to seek the generalization of the system for its use in a wide age range of the population through a parametric analysis of anthropometry based on anthropometric indices of the Latin and U.S. population [82],[83], and an isometric strength normative database of quantitative muscle testing for joint torque force [84].

Table 4. Qualitative and quantitative design criteria.

		Advantages	Disadvantages
Type of device	Final effector	Does not depend on the length of the human arm, the inclusion of a higher percentage of people	Limited movement according to dimensions
		Easy to manufacture	Cannot move each joint independently
			It is necessary to estimate the position of the joints, which cannot be directly measured
	exoskeleton	The movement occurs directly in the patient’s joints.	Depends on anatomical lengths of patients, exclusion criteria
		Independent movement for each joint	Increased manufacturing complexity
		Independent control of each junction, independent measurements
Type of chain	Open	Wide movement regardless of device dimensions	Increased susceptibility to external forces and inertia
	Close	Major stability against external forces	Movement limited by the dimensions of the device
Type of transmission	Rigid	Direct connection with the drive shaft, avoids possible losses due to friction or elasticity.	Possible fractures in the structure due to unforeseen shocks
		Space optimization
	Elastic	Quieter movements	Possible sliding under forces greater than supported
		Absorbs shocks in the transmission	Large dimensions
		Easy disengagement and maintenance
		Min	Max
Dimensional parameters	Height	1.47 m	1.93 m
	Body mass	46.7 Kg	124.7 Kg
	Upper limb weight	2.335 Kg	6.235 Kg
	Arm length	0.27 m	0.41 m
	Arm perimeter	0.23 m	0.34 m
	Forearm length	0.21 m	0.33 m
	Forearm perimeter	0.21 m
	Sidearm length	0.65 m	0.82 m
	Elbow width	0.055 m	0.074 m
	Elbow to elbow width	0.34 m	0.7 m
	Hand length	0.15 m	0.19 m
	Wrist width	0.045 m	0.06 m
	Hand width	0.069 m	0.091 m
	Joint and movement	Approx. torque + standard deviation (N) in women	Approx. torque + standard deviation (N) in male
Functional parameters	Shoulder adduction	28.4 $\pm$ 7.5	51.3 $\pm$ 17.7
	Shoulder flexion	30.4 $\pm$ 8.7	55.0 $\pm$ 17.6
	Shoulder extension	34.3 $\pm$ 11.2	73.5 $\pm$ 27.9
	Shoulder internal rotation	19.4 $\pm$ 4.6	41.1 $\pm$ 10.1
	Shoulder external rotation	20.7 $\pm$ 5.2	38.3 $\pm$ 9.1
	Elbow flexion	39.4 $\pm$ 7.7	70.9 $\pm$ 15.9
	Elbow extension	22.0 $\pm$ 4.7	44.3 $\pm$ 9.8
	Hand grip	250.4 $\pm$ 54.8	411.3 $\pm$ 73.5

According to the aspects listed in Table 4, (1)(1) $$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)={\tau }_{\mathit{\text{total}}}$$(1) For the type of device, an exoskeleton is more appropriate, the most important reason being that the motion is applied directly to the joint and reduces the need to estimate positions and velocities as it would in an end-effector system. (2)(2) $$M(q)=\sum _{i=1}^n(m_i{J}_v^{\mathit{\text{iT}}}{J}_v^i+J_{\omega }^{\mathit{\text{iT}}}{R}_i{\tilde{I}}_i{R}_i^T{J}_{\omega }^i)$$(2) For the type of chain it may be indifferent if the conditions for ease of design and workspaces are preserved. In our case, an open chain was chosen due to the complexity of the system design for the entire upper limb, and the that range of amplitude of all joints would be limited with a closed chain also considering the singularities that may appear [85],[86]. (3)(3) $$G(q)=-\sum _{i=1}^n{J}_v^{\mathit{\text{iT}}}(q)m_i{g}_0$$(3) The type of transmission is indifferent, but it also depends on the application and the amount of stress to which both the motor and the structure where the motor is anchored. In this case, the motion studies and the technical characteristics of the motors will define how much load will be necessary to satisfy the need and whether the design dimensions allow the implementation of elastic transmissions, optimizing spaces without sacrificing amplitude in the mobility ranges. (4)(4) $$\begin{array}{c}{c}_{\mathit{\text{ij}}}=\sum _{k=1}^n{c}_{\mathit{\text{ijk}}}\stackrel{.}{q_k}\\ c_{\mathit{\text{ijk}}}=\frac{1}{2}\left(\frac{\partial m_{\mathit{\text{ij}}}}{\partial q_k}+\frac{\partial m_{\mathit{\text{ik}}}}{\partial q_j}-\frac{\partial m_{\mathit{\text{jk}}}}{\partial q_i}\right)c_{\mathit{\text{ijk}}}=c_{\mathit{\text{ikj}}}\end{array}$$(4) The dimensional parameters define to a large extent the design specifications of the robotic system since they allow the establishment of dimensional criteria in the design based on anthropometric studies of the target population. These dimensional criteria have maximum and minimum values that the robotic system must comply with. This is an aspect of adaptability and generalization within the target population. (5)(5) $${\tau }_{\mathit{\text{total}}}=\tau -f_{\mathit{\text{ext}}}-f(q,\dot{q})$$(5) Functional parameters set specifications in terms of maximum torques and drive systems, design specifications are highly dependent on motion studies, along with the technical characteristics of the motors to be used in the robotic system.

Additionally, it is important to consider the design of bilateral systems i.e. systems with an option for arm-switching configuration. For end-effector-based systems, bilateral design and implementation is much simpler because the anchor point between the system and the upper limb is usually through the hand grip, making it easier to switch the system for the required arm. Works such as [35]–[40] have implemented bilateral training in end-effector-based systems. For the case of exoskeletons, the design is more complex, and in order to implement this attribute, the option to duplicate the robotic system for the opposing limb can be considered as in [23],[41], or also, the same system for one limb can be adapted for the opposite limb by means of an arm-switching configuration. This configuration is not immediate, depends on the design, and requires guidance to perform it, however, it reduces costs and adds attributes in adaptability. Especially if its use is for physical rehabilitation applications. The best-known system with this configuration is Hocoma’s Armeo Power system [42],[43].

3.3. Workspace and degrees of freedom

The present work seeks to optimize workspaces and degrees of freedom in the design of robotic systems for upper limb rehabilitation. In terms of manipulability, in the literature we find systems such as the ANYexo [20] that claim to increase manipulability in the workspace compared to other systems such as Harmony [87] and ARMin III [88]. However, there is still mobility limitation in some movements such as shoulder abduction-adduction due to mechanical constraints to avoid collisions with the patient. This section demonstrates how to ensure the range of workspace, reflected in all upper limb movements considered for this mechanical design.

From the ranges of mobility defined in Table 1 the workspace of the entire upper limb is constructed by identifying the maximum points of the range of the upper limb in the frontal, transverse, and sagittal planes as shown in Figure 3.

Figure 3. Composition of upper limb workspace based in AAOS.

The design of the robotic system must then be adjusted to the defined workspace. The challenge now is a design that preserves spatial specifications, adaptability to people with different anthropometric proportions, collision avoidance with the robotic system, and configuration for arm switching. The following aspects play a very important role in the design to guarantee the workspace: (1)(1) $$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)={\tau }_{\mathit{\text{total}}}$$(1) Number of degrees of freedom, (2)(2) $$M(q)=\sum _{i=1}^n(m_i{J}_v^{\mathit{\text{iT}}}{J}_v^i+J_{\omega }^{\mathit{\text{iT}}}{R}_i{\tilde{I}}_i{R}_i^T{J}_{\omega }^i)$$(2) Optimization of the design space is restricted by the type of actuator used, and (3)(3) $$G(q)=-\sum _{i=1}^n{J}_v^{\mathit{\text{iT}}}(q)m_i{g}_0$$(3) The validation of points 1 and 3 requires heuristic strategies that can be obtained by means of physical scale models or simulation models. In our case, we verified this strategy using both methods focused mainly on the elbow joint because it is a compound joint where several movements are generated on the same point (flexion-extension, adduction-abduction, flexion-horizontal extension, internal-external rotation and protraction-retraction (scapulohumeral)).

The design of the system suggests a minimum of 6 degrees of freedom (DoF), since, as mentioned above, the exercise schemes defined in Tables 2 and 3 show the use of the elbow joint, and also the other joints of the upper limb described in Figure 1. In our case, we consider the protraction-retraction movements as a complement to the horizontal shoulder flexion-extension movements in order to reach the full range of amplitude in the transverse plane. Consequently, the design will be oriented to a redundant 7 DoF robotic system. The procedure is as follows: We start from a conceptual design where we define an initial order of the axes of actuation as shown in Figure 4a. Subsequently, we transfer the concept to a physical scale model so that we can visually analyze the options for the order and alignment of the axes with the shoulder as shown in Figure 4b. The configuration in the scale model suggests an organization of the axes of action as follows: (1)(1) $$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)={\tau }_{\mathit{\text{total}}}$$(1) protraction – retraction (scapulo-humeral), (2)(2) $$M(q)=\sum _{i=1}^n(m_i{J}_v^{\mathit{\text{iT}}}{J}_v^i+J_{\omega }^{\mathit{\text{iT}}}{R}_i{\tilde{I}}_i{R}_i^T{J}_{\omega }^i)$$(2) flexion – horizontal extension (gleno-humeral), (3)(3) $$G(q)=-\sum _{i=1}^n{J}_v^{\mathit{\text{iT}}}(q)m_i{g}_0$$(3) flexion – extension (gleno-humeral), (4)(4) $$\begin{array}{c}{c}_{\mathit{\text{ij}}}=\sum _{k=1}^n{c}_{\mathit{\text{ijk}}}\stackrel{.}{q_k}\\ c_{\mathit{\text{ijk}}}=\frac{1}{2}\left(\frac{\partial m_{\mathit{\text{ij}}}}{\partial q_k}+\frac{\partial m_{\mathit{\text{ik}}}}{\partial q_j}-\frac{\partial m_{\mathit{\text{jk}}}}{\partial q_i}\right)c_{\mathit{\text{ijk}}}=c_{\mathit{\text{ikj}}}\end{array}$$(4) adduction – abduction (gleno-humeral), (5)(5) $${\tau }_{\mathit{\text{total}}}=\tau -f_{\mathit{\text{ext}}}-f(q,\dot{q})$$(5) elbow flexion – extension, (6)(6) $$f(q,\dot{q})=F_s\mathit{\text{sgn}}(\dot{q})+F_v\dot{q}$$(6) wrist pronation - supination, and (7)(7) $$f(q)\approx f(q_k)+J(q_k)(q-q_k)$$(7) wrist flexion-extension. With these configurations, a simple CAD model is constructed to confirm the range of the system in the previously described workspace. In Figure 5 a simple conceptual design of the 7 DoF system is shown considering the boundary positions of the workspace, the proposed configuration satisfies the workspace of the upper limb and does not generate collisions in maximum amplitudes of movements such as abduction, extension and horizontal flexion of the shoulder.

Figure 4. Conceptual design and location of actuators of the shoulder joint.

Figure 5. Conceptual design of the 7 DoF system in boundary positions of the human workspace.

3.4. Kinematic and dynamic formulation

We obtain the kinematic and dynamic model of the proposed 7-Dof robotic system. The axis configuration mentioned in the previous section is used. Figure 6 shows the basic model of the system with its respective motions and the diagram with the corresponding variables and axes for the calculation of the transformation matrices and the Jacobian $J(q)$ through the Denavit-Hartenberg convention. Subsequently, the dynamic formulation of the assistive robotic system is obtained. We use the dynamic model in joint space as follows, (1) $$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)={\tau }_{\mathit{\text{total}}}$$(1) where q is a vector $R^{7x1}$ of generalized articular coordinates, $M(q)$ is the inertia matrix $R^{7x7},$ $C(q,\dot{q})$ is the Coriolis matrix $R^{7x7},$ $G(q)$ is the vector of gravity forces $R^{7x1}$ (due to the weight of each link) and ${\tau }_{\mathit{\text{total}}}$ is the vector of generalized forces (non-conservative) $R^{7x1}.$ The inertia matrix $M(q)$ is obtained as follows, (2) $$M(q)=\sum _{i=1}^n(m_i{J}_v^{\mathit{\text{iT}}}{J}_v^i+J_{\omega }^{\mathit{\text{iT}}}{R}_i{\tilde{I}}_i{R}_i^T{J}_{\omega }^i)$$(2) where $m_i$ is the mass of the link i, $v_{\mathit{\text{ci}}}$ is the velocity of the center of mass of the link i, ${\omega }_i$ is the angular velocity of the center of mass of the link i ${\tilde{I}}_i$ is the constant inertia tensor, $J_v^i(q)$ is the linear velocity component of the Jacobian matrix at the link i and $J_{\omega }^i(q)$ is the component of the angular velocity of the Jacobian matrix at the link i. The vector of gravity forces $G(q)$ is obtained as, (3) $$G(q)=-\sum _{i=1}^n{J}_v^{\mathit{\text{iT}}}(q)m_i{g}_0$$(3)

Figure 6. Conceptual design and kinematic model of the 7-DoF robotic assistive system.

Where $G_i(q)$ is the moment of inertia of the joint i due to gravity. Then, the Coriolis matrix $C(q,\dot{q}),$ can be obtained from the Euler-Lagrange formulation using first-order Christoffel symbols $c_{\mathit{\text{ij}}}$ as, (4) $$\begin{array}{c}{c}_{\mathit{\text{ij}}}=\sum _{k=1}^n{c}_{\mathit{\text{ijk}}}\stackrel{.}{q_k}\\ c_{\mathit{\text{ijk}}}=\frac{1}{2}\left(\frac{\partial m_{\mathit{\text{ij}}}}{\partial q_k}+\frac{\partial m_{\mathit{\text{ik}}}}{\partial q_j}-\frac{\partial m_{\mathit{\text{jk}}}}{\partial q_i}\right)c_{\mathit{\text{ijk}}}=c_{\mathit{\text{ikj}}}\end{array}$$(4) where n is the number of DoF, $m_{\mathit{\text{ii}}}$ is the moment of inertia of the $i-\mathit{\text{th}}$ joint, when the other joints do not move. $m_{\mathit{\text{ij}}}$ is the $i-\mathit{\text{th}}$ joint acceleration effect at the joint j (coupling effect), $c_{\mathit{\text{ijj}}}{{\dot{q}}_j}^2$ is the centrifugal force on the joint i due to the $j-\mathit{\text{th}}$ speed of articulation and $c_{\mathit{\text{ijk}}}{\dot{q}}_j{\dot{q}}_k$ is the coriolis effect in the $i-\mathit{\text{th}}$ articulation due to the $j-\mathit{\text{th}}$ and $k-\mathit{\text{th}}$ joint velocity.

The components of the generalized forces are then defined ${\tau }_{\mathit{\text{total}}}$ as follows, (5) $${\tau }_{\mathit{\text{total}}}=\tau -f_{\mathit{\text{ext}}}-f(q,\dot{q})$$(5)

Where $\tau$ is the torque applied (by the actuators) to the joints, $f_{\mathit{\text{ext}}}$ is the pair of external forces/momentum and $f(q,\dot{q})$ is the torque due to friction in the joints defined as (6) $$f(q,\dot{q})=F_s\mathit{\text{sgn}}(\dot{q})+F_v\dot{q}$$(6)

Where $F_s$ is the static friction matrix and $F_v$ is the viscous friction matrix [59],[89].

If the reader is interested to know more about the formulation of the robot modeling and integration with an AAN-based control model, please refer to [90].

3.4.1. Inverse kinematics

In order to accurately determine the inverse kinematics for the robotic system, it is crucial to consider the characteristics of the robot, since it is a redundant 7-DoF system, multiple solutions can appear for $q_i,i=1\mathrm{\dots }n(\mathit{\text{GDL}}),$ where n joints: $q=(q_1,q_2,q_3,q_4,q_5,q_6,q_7),$ and m variables in cartesian space: $(P{e}_x,P{e}_y,P{e}_z,\alpha ,\beta ,\theta ).$ Then, a robot is redundant with respect to the cartesian space when $n>m$

Since the proposed system is redundant, to obtain the inverse kinematics it is necessary to apply multi-variable approximation methods. In our case, the Newton method and the gradient method are applicable [91]–[93].

Newton’s method seeks to minimize the error between the desired end-effector variables and those obtained from the direct kinematics product of the joint variables by means of Taylor approximations. (7) $$f(q)\approx f(q_k)+J(q_k)(q-q_k)$$(7)

Rearranging and assuming J squared and invertible (pseudo-inverse), we obtain the solution such that $(q=q_{k+1}):$ (8) $$q_{k+1}=q_k+J^{-1}(q_k)(x_d-f(q_k))$$(8)

The algorithm will stop when: the Cartesian error is small $|(|x_d-f(q_k)|)|<ϵ$ or when the joint increment is small $|(|q_{k+1}-q_k|)|<ϵ$

Finally, the general equation with Newton’s method results in: (9) $$q_{k+1}=q_k+J{(q_k)}^{-1}(x_d-p_7^0(q))$$(9)

Random initialization values are taken for $q_i,$ where $i=1\mathrm{\dots }7(\mathit{\text{DoF}})$ and define $(x_d-f(q_k))<ϵ$

Alternatively, the gradient method defines a loss function where minimization is performed by negative gradient movement to achieve convergence in an iterative manner. (10) $$q_{k+1}=q_k-\alpha \nabla g(q_k)$$(10)

Where $\alpha$ is the step size of $g(q)$ for each iteration, then we define a scalar error function (11) $$g(q)=\frac{1}{2}\left|\right|x_d-f(q)|{|}^2=\frac{1}{2}{(x_d-f(q))}^T(x_d-f(q))$$(11) (12) $$\nabla g(q)=-{\left(\frac{\partial f(q)}{\partial q}\right)}^T(x_d-f(q))$$(12)

Integrating, Eqs. (10)–(12)(12) $$\nabla g(q)=-{\left(\frac{\partial f(q)}{\partial q}\right)}^T(x_d-f(q))$$(12) , the general equation of gradient method is, (13) $$q_{k+1}=q_k+\alpha J{(q_k)}^T(x_d-f(q_k))$$(13)

3.5. Motion study and torque acquisition

Then, the maximum torques required for each joint are determined. The shoulder movements require more effort due to the weight of the next joints. Therefore, in this shoulder joint, the analysis is performed to determine the last design criterion: the optimization of the design space defined by the actuator and the type of transmission (elastic, rigid).

To carry out the simulation, an initial weight is assigned to the links of the CAD model using an average weight per link of 1.5 Kg. As a design criterion, the weights are oversized by an additional 40%, this oversizing is based primarily on the variability of the manufacturing material. The objective is to determine which printable material provides better performance. We use a ratio calculation between the densities of the less dense printable material (Polypropylene = 0.9 g/cm³), and the denser printable material (Nylon = 1.52 g/cm³). Thus, $1-(0.9/1.52)\approx 0.41.$ Due to manufacturing, there may be variations in dimensions and material properties. Additionally, the weight of the human arm is incorporated taking as reference the maximum dimensional parameters of Table 4. Flexion-extension, abduction-adduction, and horizontal shoulder flexion-extension movements are considered for the simulation. From the motion analysis, an approximation of the maximum torques is obtained. These torques will be used as a reference for the selection of the actuators and will later serve as a criterion to minimize spaces and reduce weights in the design of the robotic assistance system. The results obtained are shown in Figure 7a–d.

Figure 7. Theoretical torques from motion analysis.

Notice that the ${\theta }_1$ Protraction – retraction (scapulohumeral) and ${\theta }_2$ Flexion – horizontal extension (glenohumeral) joints reach maximum values of 12 Nm. While ${\theta }_3$ Flexion – extension (glenohumeral) and ${\theta }_4$ Adduction – abduction (gleno-humeral) joints, the required torques reach values of 66 Nm and 54 Nm respectively. This implies that the actuators chosen must satisfy these torques or, alternatively, use torque multiplication drives.

The torques obtained are purely theoretical and will involve a reduction of the design dimensions of the robotic system in order to reduce the demand of the motors on the therapy routines, the weight of the patient’s arm, and the weight of the robotic assistance system itself.

3.6. Actuator selection

The selection of the actuation allows the establishment of dimensional specifications in the design. To make this process the following criteria are considered:

• Maximum torque required

• Weight and size of the actuator

• Built-in gearbox

• Built-in controller

• Cost

Table 5 presents a comparison of features of the commercial actuators, where we list the actuator weight $(\mathit{\text{Kg}}),$ the continuous and maximum torque provided $(\mathit{\text{Nm}}),$ the controller card included, the transmission box included, and the retail price.

Table 5. Commercial actuator comparison.

Actuator	Weight	Continuous torque (Nm)	Max. torque (Nm)	Controller board	Gearbox	Price
FHA-C Mini Actuator (8 C/11C/14C)	410	0.8/1.3/2.7	1.8/3.3/4.8	yes	yes	Not released
	630	0.8/1.3/2.6	4.5/8.3/11
	1200	0.8/1.4/2.9	9.0/18/28
Maxon Exoskeleton joint actuator Drive GEN.1	Not released	54	120 at 20% duty cycle	yes	yes	Not released
X-Series Actuator (X5-1/X5-4/X5-9/X8-3/X8-9/X8-16)	300	1.3	2.5	yes	yes	3.000–3500 USD
	354	4	7
	360	9	13
	455	3	7
	475	8	20
	490	16	38
RMD-X8 Servo Motor (Normal/pro)	610	3.5	24	yes	yes	402–489 USD
	730	6.9	40
Dual shaft motor - D6374 150KV	1680	35 approx. depending on gearbox	55 approx. depending on gearbox	No	No	308 USD approx.
OpenTorque Actuator	1150	Not specified	80	No	Yes	338 USD Approx.

The analysis of the comparative table allowed us to deliberate on the decision to choose the actuators. Finally, we opted for RMD-X8 pro bushels actuators due to their weight-price ratio analyzed in Table 5. Additionally, these actuators meet the selection criteria defined previously. The actuators will be for the shoulder and elbow joints, and for the wrist joint, the RMD L-5015 actuators are considered. These actuators are provided with a transmission box; however, the theoretical torque results obtained in Figure 7a–d suggest adding a transmission stage that can either be elastic or rigid. With these considerations, we proceed to the mechanical design of the upper limb assist robotic system.

4. Mechanical design: upper limb robotic assistive system

For the design of the robotic assistive system, we start from the conceptual model in Figure 5. A good start for the design of mechanical systems is to place in the design software all the commercial components to be included. In the structural development of the arm system, actuators are a key component where drawers, housings, brackets, and bases are designed, and a reduction of spaces is performed accordingly with the dimensions of the actuators.

We start designing from the distal to the proximal part of the upper limb. The actuator is placed in the same orientation of the movement to be executed as shown in Figure 8, taking into account the design criteria in Table 4 we start by designing the wrist part starting with the grip, the first joint movement (wrist flexion-extension) and the second joint movement (wrist pronation-supination) as shown in Figure 8. A hand grip adjustable to different hand sizes by means of a hand gear is considered. To perform the wrist flexion-extension movements, it is designed in such a way that the axis of motion between the robotic system and the wrist are aligned.

Figure 8. Wrist flexion-extension and pronation-supination design.

Subsequently, the forearm section and the second wrist movement are designed. The forearm has two support points, one in the proximal part of the forearm and the other in the distal part. The actuator to perform the wrist protraction-retraction movements is located on the distal part of the forearm. The designed system has a semicircular rail propelled by a belt. The rail has a carriage that slides and rotates concentrically with the midpoint of the semicircle of the rail. This point coincides with the axis of movement of wrist pronation-supination.

The proximal part of the forearm has two support rods for length acting as a linear rail through a worm screw. This allows the operator to correct the length of the robotic forearm according to the length of the patient’s forearm. Finally, a configuration gear is designed for the arms change. This allows the operator to rotate the forearm-wrist-grip complement at a $180°$ angle about the elbow joint. This option has only been seen on Hocoma’s Armeo Power system; however, we have reduced the weight and size of the system without reducing robustness from stress studies.

Then we design the next joint (elbow flexion-extension), from here, the RMD-x8 pro actuators are arranged. In the same way, the actuator is positioned to align the movement of the motor with the elbow. A belt drive is used to take advantage of the space and material reduction of the L-shaped housing design. The support is connected to the output shaft; another linear rail is arranged for correcting the length of the robotic arm according to the length of the patient’s arm, as shown in the design in Figure 9.

Figure 9. Elbow flexion-extension design.

The design of the movements associated with the gelno-humeral shoulder joint (flexion-extension, horizontal flexion-extension, and abduction-adduction) is presented hereafter. We use the same order in the arrangement of the actuators considered in the conceptual design of Figure 4a. The design consists of three actuators that share the same frontal plane. The mechanism is locked to execute the arm change configuration. This mechanism allows to release on an axis of the shoulder arm to rotate it $180°.$ The design is shown in Figure 10. Notice that the actuators associated with the flexion-extension and abduction-adduction movements require planetary transmission. This occurs because with this configuration a higher torque multiplication factor than with belt transmission is obtained, which can be observed from Figure 7c,d. The transmission address a 1:8 ratio, which will mean a significant increase of the torque at these joints. As it is a rigid transmission, helical gears are handled to reduce noise compared to spur gears. On the other hand, the actuator that performs the horizontal bending-extension movements does not require a substantial increase in torque, so a belt drive is enough since this movement is performed in the transverse plane, so effects of gravity will not affect.

Figure 10. Shoulder adduction-abduction, flexion-extension and horizontal flexion-extension design.

The movement of the shoulder in the scapulo-humeral part is an extension of the horizontal flexion-extension movements of the shoulder. So similarly, a belt transmission will be enough for the motion since this movement is also performed in the transverse plane. This section is crucial because it supports the entire weight of the robotic arm and the human arm. A reinforcement support that is directly connected to the main base of the assistive system is considered. The base is composed of a structural system of aluminum alloy beams connected by aluminum bends. The corresponding design is shown in Figure 11.

Figure 11. Shoulder protraction-retraction design.

Finally, the base of the robotic system is designed. This part is composed of a structural network of beams in the shape of an inverted T, where the base of the robotic arm is housed in the upper part and functions as a rail to correct the alignment height with respect to the patient’s height. Rail guides are driven by linear bearings. The movement is actuated by two linear actuators of 200 N. The electronics, power supplies, control systems, and ventilation are located in the lower part. This choice gives more stability and robustness to the base of the robotic system. Finally, beaver-type wheels are included to move the robotic system as needed. The design of this section is shown in Figure 12.

Figure 12. Principal base design.

Finally, we present the complete assistive robotic system in left arm and right arm configuration, and in rendering in Figure 13.

Figure 13. Complete robotic assistive system design and arm switching configuration.

4.1. Selection of materials and FEM stress study

Once the model of the robotic assistive system has been defined, we evaluate the materials to manufacture and build it. A study of materials will determine which is the most suitable option. We considered aspects such as lightness, robustness, hardness, and durability. However, in medicine and rehabilitation, there are regulations for the selection of medical devices’ materials, tools, and elements that interact directly with patients. Metals such as stainless steel, titanium, or aluminum, ceramics, polymers, composites, and biomaterials are the most used in the medical and rehabilitation industry [27],[28]. There are some additional issues that will help determine the most suitable material for this application. While one can easily choose to use titanium, steel, or aluminum, the issues that can rule out a choice are manufacturing costs, material costs, and material weight.

Thus, one of the advantages of using plastics in medicine is their relatively low cost compared to metallic materials. Plastics can be molded into useful configurations that would be difficult or impossible to duplicate in metals and can be fabricated using technologies such as 3D printing. Also, some composites are strong and flexible. The most commonly used resins in medical plastics are polyvinyl chloride (PVC), polyethylene, polypropylene, and polystyrene. But polycarbonates, ABS, polyurethanes, polyamides, thermoplastic elastomers, polysulfones, and polyetheretheretherketone (PEEK) are finding specialized applications in medical devices, especially when high performance is required. Polyetheretheretherketone (PEEK) resins are increasingly replacing titanium, ceramics, and other resins in orthopedic implant applications.

The incorporation of plastics in modern medicine has steadily increased over the last decade. Plastics have contributed to a reduction in medical costs and infectious diseases. High-tech polymers are used to create new and improved artificial limbs, and plastic devices [94]–[96].

Therefore, as a preliminary study of materials, we performed a comparative study of stresses between plastics that meet the criteria for use in medical applications in terms of ease of fabrication, manufacturing costs, and weight of the part. As simulation criteria, we defined the maximum average weight of each joint, including the human arm, plus an isometric torque load produced by the patient’s force, and finally, a $50\%$ of the total value is added as a safety factor. Table 6 shows the parameters for the stress simulation.

Table 6. Defined loads for the finite element analysis.

Joint	max weight of robot + human joint section (Kg)	Approx Average joint torque (N)	total load +50% (N)
Base	19	50	354
Shoulder flexion-extension	13.5	50	273
Shoulder Abduction-adduction	14	50	280
Elbow	9.4	70	243

Finally, the stress study is carried out by evaluating one of the parts with the highest susceptibility to mechanical failure, which is the main rail support that supports the entire weight of the robotic arm shown in Figure 11. The analysis was performed for ABS, PLA, HIPS, PETG, Nylon, ASA, Polycarbonate, Polypropylene, and Nylon X materials. Nylon X has been one of the revelations in terms of 3D printing. It consists of nylon reinforced with micro-carbon fibers of relatively easy printing, capable of printing parts with rigidity, impact resistance, and high tensile strength as it is considered an “engineering grade” material. Figure 14 presents the results of the stress study showing the Von Mises stress values in $N/m^2$ and the resulting displacement deformation in mm. Observe that for the loads induced in the simulation, NylonX stands out as the material with the lowest Von Mises stress value. (2.86 × 10⁷ N/m²) and much lower deformation than other materials (0.33 mm). Additionally, Nylon X is an emerging material for engineering use and is easy to manufacture by using 3D printing technologies, we consider Nylon X as the material selected for the manufacturing of the robotic system.

Figure 14. Von mises stress and URES deformation comparison results with FEA.

Once the material is selected, a second torque analysis of the motors is performed, verifying that the selected motors have enough torque to move the system with the chosen material. The RMD-x8 Pro motors have an experimental nominal torque of 11Nm. Implementing the same simulation routine, the maximum torques of the shoulder and elbow movements are obtained. These torques are compared with the real values of the motors including the transmission in Table 7.

Table 7. Simulated vs experimental peak torque.

	Simulated peak torque (Nm)	Experimental peak torque (Nm)
Shoulder scapulohumeral protraction-retraction	9.4	19
Shoulder glenohumeral horizontal flexion-extension	2.5	19
Shoulder glenohumeral flexion-extension	23	88
Shoulder glenohumeral abduction-adduction	23	88
Elbow flexion-extension	5.5	19

5. Conclusions

In this article, we present several guidelines to establish the design criteria for a robotic system to assist in the rehabilitation of the upper limb. We analyzed the physiological, biomechanical, and technological components associated with the pathology to establish design specifications and recommendations for the construction of the robotic system. We have carried out motion simulation studies where we managed to increase the workspace and joint mobility ranges involved in the design. Subsequently, we performed an analysis of the appropriate selection of materials based on stress studies. We identified some qualitative and quantitative design criteria that are of great importance in the design of physical rehabilitation systems. We also determined the complete working space of the upper limb and built conceptual and mathematical models of the system. We consider practical aspects in the selection of actuation and emerging technologies and materials to reduce system weight, manufacturing costs, and material costs with the use of 3D printing technologies and materials such as NylonX, also verifying the critical values (torque and weight) with the selected material, which allows us to finally propose a never seen before arm change configuration. In this way, we defined the design specifications and construction characteristics that resulted in a 7-degree of freedom system with a novel configuration system for arm change for the treatment of both arms.

Based on an anthropometric and physiopathology analysis of the joint, we defined the parametric characteristics related to model type selection, performance selection, material selection, and dimensional aspects of design. This allowed the development of design strategies for a reduction of the dimensional spaces of the parts and a reduction of weight using emerging materials such as Nylon X. Our design starts from the premise of building mechanical systems for rehabilitation using alternative materials to metal and meeting rigorous tests for strength and durability, which implies a reduction in manufacturing costs by using emerging technologies such as 3D printing. In a series of selected printable materials, the results determined that Nylon X, in addition to HIPS, is one of the materials with the highest stress resistance at 2.86 × 10⁷ N/m² and the lowest deformation at 0.33 mm.

These recommendations and criteria serve as a starting point in the systematization of the mechanical design processes of robotic systems for physical assistance or rehabilitation. Future work will be oriented to the fabrication of the robotic assistive system, and to the improvement of the system as observed in practice.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is funded by Universidad Militar Nueva Granada- Vicerrectoría de Investigaciones, under research grant for project IMP-ING-3127, entitled ’Diseño e implementación de un sistema robótico asistencial para apoyo al diagnóstico y rehabilitación de tendinopatías del codo’.

Notes on contributors

Andrés Guatibonza

Andrés Guatibonza, is Mechatronic Engineer from Militar Nueva Granada University – Colombia. He worked as a research assistant at Militar Nueva Granada University. His main research areas are in robotics, mechanical design, and design of mechatronic systems. He is currently associate as a graduate assistant and Doctoral student at Militar Nueva Granada University, Bogotá, Colombia.

Carlos Zabala

Carlos Zabala, is Mechatronic Engineer from Militar Nueva Granada University – Colombia. He worked as a research assistant at Militar Nueva Granada University. His main research areas are in human-machine interfaces and design of mechatronic systems. He was associated as a advisor at Militar Nueva Granada University, Bogotá, Colombia.

Leonardo Solaque

Leonardo Solaque, is Electronic Engineer from University of Antioquia – Colombia. He studied the Master in Electrical engineering at Los Andes University - Colombia. He obtained the Ph.D. in Automatic Control in 2007 from LAAS-CNRS and INSA of Toulouse - France. His main research areas are in control system, robotics, path planning, filter system and sensory fusion. He is currently associate professor in the Mechatronics Department at Militar Nueva Granada University, Bogotá, Colombia.

Alexandra Velasco

Alexandra Velasco, is Electronic Engineer and Master in Electronics engineering from Javeriana University. She obtained the Ph.D. in Robotics, Automation, and Bioengineering in 2015 from Pisa University. Her main research areas are in Control and Robotics focused on rehabilitation systems, trajectory planning, and optimization. She is currently assistant professor in the Mechatronics Department at Militar Nueva Granada University, Bogotá, Colombia.

Lina Peñuela

Lina Peñuela, is Electronic Engineer and Master in Electronics engineering and computing from Los Andres University - Colombia. Her main research areas are in electronics, sensors and biomedical systems. She is currently assistant professor in the Mechatronics Department at Militar Nueva Granada University, Bogotá, Colombia